Demands for high-precision measurements of a circuit element are increasing annually. The apparatus for such measurements is exemplified by the "Multi-Frequency LCR meter 4274A or 4275A" which is commercially available from Yokogawa-Hewlett-Packard for use in four-terminal measurements. FIG. 1 is a schematic circuit diagram showing a circuit element measuring apparatus for four-terminal pair measurements according to the prior art.
By means of four terminal lines CL.sub.1, CL.sub.2, CL.sub.3, and CL.sub.4 providing four terminal pairs, a circuit element to be measured (hereinafter referred to as a "DUT" or element Z.sub.x) is connected to a signal source SS, a volt meter VM, range resistance R.sub.r and zero detection amplifier A which together form a measuring apparatus. The impedance value of the element Z.sub.x shall also be referred to as Z.sub.x.
The lines CL.sub.1, CL.sub.2, CL.sub.3 and CL.sub.4 are generally made of coaxial cables although not limited thereto, and their outer conductor terminals g.sub.11, g.sub.21, g.sub.31 and g.sub.41 at one end thereof are connected to one another and held at the same potential. The terminals l.sub.11 and l.sub.21 of the center conductor of the lines CL.sub.1 and CL.sub.2 at the same end thereof are connected to one terminal of the element Z.sub.x. The terminals l.sub.31 and l.sub.41 of CL.sub.3 and CL.sub.4 are connected to the other terminal of the element Z.sub.x. The terminals of the center conductors of the lines CL.sub.1, CL.sub.2, CL.sub.3 and CL.sub.4 and the outer conductor at the opposite end (i.e. at the side on the meter) are respectively designated as l.sub.12, g.sub.12, l.sub.22, g.sub.22, l.sub.32, g.sub.32, l.sub.42 and g.sub.42.
Between the terminals l.sub.12 and g.sub.12, the signal source SS and a signal source resistance R.sub.s are connected in series. The volt meter VM is connected between the terminals l.sub.22 and g.sub.22. The terminals l.sub.22 and g.sub.32 are respectively connected to the inverted input terminal and non-inverted input terminal of the zero detection amplifier A. The feedback resistance R.sub.f is connected between the inverted input terminal and the output terminal of the zero detection amplifier A. The output of the zero detection amplifier A is introduced into a narrow-band amplification/phase compensation amplifier NBA. The output of the NBA is applied through the range resistance R.sub.r to the terminal l.sub.42. The NBA is similar to that used in the aforementioned meters 4272A and 4275A. The range resistance R.sub.r is placed between the terminal l.sub.42 and the NBA output, and the terminals g.sub.42 and g.sub.32 are also connected.
In the circuit of FIG. 1, an automatic control is performed on the voltage between the terminals l.sub.32 and g.sub.32, i.e., controlled such that the current flow through the terminal l.sub.32 may be substantially zero. As a result, a voltage V.sub.x to be applied to the element Z.sub.x is obtained as the indication of the volt meter VM. Moreover, a current I.sub.x to flow through the element Z.sub.x is obtained as an indication of the range resistance R.sub.x. Since a complex voltage and a complex current are measured at the volt meter VM and the range resistance R.sub.r with reference to the detected output of the signal source SS, the value Z.sub.x is determined in a complex value in accordance with the following equation: EQU Z.sub.x =V.sub.x /I.sub.x =V.sub.x R.sub.r /V.sub.i ( 0)
wherein V.sub.i is equal to the voltage generated across the R.sub.r and is expressed as EQU V.sub.i =I.sub.x R.sub.r.
In the above-equation, the term V.sub.x /V.sub.i is calculated by a well known vector voltage measuring circuit (referred to as "VRD") which is incorporated in the aforementioned meters 4274A and 4275A. The calibrations are accomplished by the well known method of shorting and opening elements lo (or by using a known third impedance) to replace the elements to be measured. However, due to a host of inaccuracies in the apparatus, the accurate value as expressed by the Equation (0) cannot always be obtained.
Specifically, the voltage V.sub.v measured by the volt meter VM is different from the voltage V.sub.x applied to the DUT. The voltage V.sub.i across the range resistor R.sub.x is also different from the product of the current I.sub.x through the DUT and the resistance R.sub.r. Moreover, the values V.sub.x and V.sub.v and the values I.sub.x and V.sub.i are respectively proportional to individual coefficients which are a function of angular frequency .omega., so that they can be expressed as follows: EQU V.sub.x =H(.omega.) V.sub.v ( 1); EQU and EQU I.sub.x =Y(.omega.) V.sub.i ( 2).
Hence, the impedance Z.sub.x of the DUT is expressed, as follows: ##EQU1##
The vector ratio of V.sub.v /V.sub.i can be accurately measured by the VRD. A known standard Z.sub.r is measured in advance in place of an unknown DUT, and the Z.sub.c (.omega.) is calculated as a correction data from the measured vector ratio (V.sub.v /V.sub.i) and the value Z.sub.R. The calculated value of Z.sub.c (.omega.) is stored in the apparatus. Thus, when the impedance Z.sub.x of an unknown DUT is to be measured, the vector ratio (V.sub.v /V.sub.i ) is measured and multiplied by the correction data Z.sub.c (.omega.).
Incidentally, in order to measure the DUT remotely or in combination with another apparatus, the impedance measuring apparatus should be able to use various cable lengths l. In order to obtain the impedance of the DUT with an optimal signal to noise or S/N ratio, a plurality of range resistors R.sub.r may be used.
From the standpoint of the S/N ratio, it is necessary to use the Z.sub.R having a value suited for the range resistance R.sub.r. It is also necessary to change the standard apparatus for each range resistance R.sub.r when the correction data Z.sub.c (.omega.) is to be obtained. However, Z.sub.c (.omega.) is a function of cable length l and range resistor R.sub.r. Therefore, it is generally necessary to measure and store the correction data Z.sub.c (.omega.) for all conceivable combinations of the value R.sub.r and l.
One conceivable solution is to determine the data Z.sub.c (.omega.) from separable and independent functions of the cable length l and the range resistance R.sub.r. The concept that the data Z.sub.c (.omega.) is determine for separable and independent functions of the cable length l and the range resistor R.sub.r means that the value Z.sub.c (.omega.) can be expressed in the form of the product of a function z1(l) of l and a function z2(R.sub.r), of R.sub.r by the following Equation: EQU Z.sub.c (l, R.sub.r, .omega.)=zl(l,.omega.)z2(R.sub.r,.omega.)(4)
The circuit measuring apparatus satisfying the above-specified definition has the following advantages:
(a) If the following three values are known for the cable lengths l.sub.1 and l.sub.2 and the range resistances R.sub.r 1 and R.sub.r 2, the correction data Z.sub.c (.omega.) need not be measured for all combinations of l and R.sub.r : EQU Z.sub.c (l.sub.1, R.sub.r 1,.omega.); EQU Z.sub.c (l.sub.1, R.sub.r 2,.omega.); EQU and EQU Z.sub.c (l.sub.2, R.sub.r 1,.omega.),
Other correction data can be calculated in the following form: ##EQU2##
In other words, the combination of the correction data to be measured is reduced as follows:
from (the number of l).times.(the number of R.sub.r) when the value Z.sub.c is not separable; PA1 to (the number of l)+(the number of R.sub.r)-1, when the value Z.sub.c is separable. As a result, the time for measuring the correction data is substantially reduced.
(b) After the correction data have been measured for one cable length l and all the range resistances R.sub.r, a correction data is measured for a new cable length. In this case, the correction data is measured for only one range resistance R.sub.r, and can be calculated from the Equation (5) for the remaining range resistance, as described in the advantage (a). In other words, the measurement of the correction data Z.sub.c (.omega.) for a new cable length may be only once by using one standard apparatus even if the range resistance R.sub.r is varied. Generally speaking, the reference resistance R.sub.R is used in the reference apparatus Z.sub.R. This means that the correction data can be easily calculated even when an arbitrary cable length l is used.
In order to achieve the advantages heretofore described, there may be several methods of making the Z.sub.c (.omega.) separable. The circuit shown in FIG. 1 satisfies the separation of the value Z.sub.c (.omega.) At point A in FIG. 1, the potential is substantially zero for a low measuring frequency signal. However, when the frequency is high, the potential at point A.sub.p in FIG. 1 is not substantially zero. In an extreme case, the potential at A.sub.p may become equal to the potential at B.sub.p in FIG. 1 as the measuring frequency or the measuring cable length l greatly increases. Whether or not the point A.sub.p reaches such a voltage depends upon the relation between the measuring cable length l and the wave length of the measurement frequency. That is, a different voltage is measured with a different cable length l even if the frequency remains the same. Assuming the separation of Z.sub.c (.omega.), the correctness of the calculated value depends upon the CMRR (i.e., Common Mode Rejection Ratio) of the differential amplifier for detecting the value V.sub.i. The accuracy of Z.sub.c (.omega. ) corresponds to a value substantially equal to the CMRR in the worst case. For example, this means a differential amplifier capable of a CMRR of 40 dB or more for 30 MHz for a circuit element measuring apparatus so that the correction data satisfies the separation of the values l and R.sub.r within an accuracy of 1% for 30 MHz. Since it is difficult to manufacture an amplifier having such an excellent CMRR, the correction data Z.sub.c (.omega.) must be measured for all the combinations of the cable length l and the range resistance R.sub.r and Z.sub.c (.omega.) is not independent.